## MA PH - Mathematical Physics

Offered By:

Faculty of Science

Below are the courses available from the MA PH code. Select a course to view the available classes, additional class notes, and class times.

**★ 3 (fi 6)(FIRST, 3-1S-0)**

Differential equations occur throughout undergraduate physics and being able to solve them is a critical mathematical skill for all physicists. The first part of the course emphasizes solution techniques to linear, second order ordinary differential equations, including series solutions and an introduction to trigonometric Fourier series via inhomogeneous equations. Nonlinear and systems of ordinary differential equations will also be discussed. The second part of the course introduces partial differential equations with a focus on the three classical linear second order partial differential equations of mathematical physics: the heat equation, the wave equation and Laplace's equation, and techniques for solving them including separation of variables, Fourier series and the d'Alembert solution of the wave equation. Examples from physics will be emphasized throughout. Prerequisite: MATH 146 or equivalent. Corequisite: MATH 214 or equivalent, and one of MATH 102 or 125 or 127. Note: Credit may be obtained for only one of MA PH 251, MATH 201, MATH 334 or MATH 336.

## Starting: 2023-09-01 MA PH 251 - Differential Equations for Physics

**★ 3 (fi 6)(FIRST, 3-1S-0)**

Differential equations occur throughout physics and being able to solve them is a critical mathematical skill for physicists. The first part of the course emphasizes solution techniques to first-order and linear, second-order ordinary differential equations, including series and Frobenius solutions, and an introduction to Fourier and orthogonal series and Sturm-Liouville problems. The second part of the course introduces partial differential equations with a study of quasilinear first-order equations, and the linear second-order wave, heat and Laplace equations, and solution techniques including the method of characteristics and separation of variables. Examples from physics will be emphasized throughout. Prerequisite: MATH 146 or equivalent and one of MATH 102 or 125 or 127. Corequisite: MATH 214 or 217. Note: Credit may be obtained for only one of MA PH 251, MATH 201, MATH 334 or MATH 336.

**★ 3 (fi 6)(FIRST, 3-0-0)**

Principles of mechanics; non-inertial frames; Lagrange's equations and Hamilton's principle; dynamics of oscillating systems; rigid body kinematics and dynamics; Hamiltonian methods and canonical transformations. Prerequisite: PHYS 244, MATH 215 or 317.

## Starting: 2023-09-01 MA PH 343 - Classical Mechanics II

**★ 3 (fi 6)(FIRST, 3-0-0)**

Principles of mechanics; non-inertial frames; Lagrange's equations and Hamilton's principle; dynamics of oscillating systems; rigid body kinematics and dynamics; Hamiltonian methods and canonical transformations. Prerequisite: PHYS 244 and one of MA PH 351, MATH 215 or MATH 317.

**★ 3 (fi 6)(SECOND, 3-1S-0)**

This final core mathematics course for physics programs covers Fourier Analysis, Vector Calculus and Complex Analysis. The first part covers generalized Fourier series and orthogonal functions, and the Fourier integral. The second part covers the operators of vector differential calculus, line and surface integrals, and the three important vector integral theorems of Green, Gauss and Stokes, with a direct application to Gauss' and Ampere's laws of electromagnetism; spherical, cylindrical and planar symmetry. The final part of the course covers the basic calculus of functions of a complex variable: the Cauchy-Riemann equations, analytic functions, the Cauchy-Goursat theorem and Cauchy integral formula, Laurent series, poles and residues, contour integration. Examples from physics will be emphasized throughout. Prerequisite: MATH 214 and one of MATH 102 or 125 or 127 and one of MA PH 251 or MATH 201 or MATH 334 or MATH 336.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Symmetries in physics; basic concepts of group theory and representation theory; finite groups; continuous groups; orthogonal and unitary groups; Lie groups; spinor representations; Lorentz and Poincare groups. Prerequisite: MATH 225 or MATH 227. Note: Credit can be obtained in at most one of MA PH 364 and MA PH 464.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Application to problems in physics of method of steepest descent, Fourier and Laplace transforms; boundary-value problems, integral equations, and Green's functions. Prerequisites: MATH 311 or 411, and 337, or equivalents.

## Starting: 2023-09-01 MA PH 451 - Mathematical Methods for Physics II

**★ 3 (fi 6)(EITHER, 3-0-0)**

Application to problems in physics of method of steepest descent, Fourier and Laplace transforms; boundary-value problems, integral equations, and Green's functions. Prerequisites: either MA PH 351 or both of MATH 311 and MATH 337.

**★ 3 (fi 6)(EITHER, 3-0-0)**

Symmetries in physics; basic concepts of group theory and representation theory; finite groups; continuous groups; orthogonal and unitary groups; Lie groups; spinor representations; Lorentz and Poincare groups. Prerequisite: MATH 225 or MATH 227.

**★ 3 (fi 6)(EITHER, 3-0-0)**

The course covers specialized topics of interest to advanced undergraduate students. Consult the Department for details about current offerings. Prerequisites depend on the subject. Credit for this course may be obtained more than once

**★ 3 (fi 6)(EITHER, 0-0-6)**

Undergraduate research project in mathematical or theoretical physics under the direction of a faculty member. Projects must involve both mathematical and physics components related to research. Prerequisites: A 300-level physics; a 300-level mathematics and consent of department. Credit for this course may be obtained more than once.

**★ 3 (fi 6)(EITHER, 3-0-0)**

This course covers specialized topics of interest to junior graduate students. Consult the Department for details about current offerings. Prerequisite: Consent of Instructor. Credit for this course may be obtained more than once.